# How to Calculate Perpetuities

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Investopedia defines a perpetuity as: "A constant stream of identical cash flows with no end." The most common perpetuity is an annuity or bond that provides indefinite payments. Many foundations are set up to provide payments to a particular cause in perpetuity. The most obvious question is how to calculate or quantify a stream of cash flows with no end. Is it even possible? If we were to take the definition literally, the answer is no. However, as for many financial concepts, a formula has been created to approximate the value.

Review the formula. The formula for a perpetuity is \$R/I%, in which R is the amount of the interest payment each period, and I is the interest rate per period.

Look at an example. In this example, you would like to set up a fund in which \$5000 a month is paid to you, starting next month. You also would like to pass this payment on to your family indefinitely. The current rate of interest is 7 percent, annually.

Define your variables. For this example, the annual payment amount (R) is \$5000 and interest (I) equals .07/12 or 0.005833333.

Calculate the present value of this perpetuity. R (\$5000) / I (0.005833333) = \$857,142.86.

Interpret the results. In narrative, this is telling you that a \$5000 perpetuity is worth \$857,142 today, compounded annually at a rate of 7 percent interest. Or, in order to create an infinite stream of monthly cash flows at \$5000, you will need to invest \$857,142 at a rate of 7 percent compounded annually.

## Tips & Warnings

• In order for the payments to start immediately, you would need to include a \$3000 payment to the total amount (\$857,142) to account for the first payment.

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